Question

a company needs to produce a label that will wrap around the lateral side of a cylindrical can. if the can is 13.9 cm tall and has a diameter of 11.6 cm, what is the area of the label that the company needs to produce? enter a decimal rounded to the hundredths place. show your work here hint: to add the pi symbol (π), type \pi\

Explanation:

Step1: Find the radius

The diameter \(d = 11.6\) cm. The radius \(r=\frac{d}{2}=\frac{11.6}{2}=5.8\) cm.

Step2: Recall the formula for the lateral surface area of a cylinder

The formula for the lateral surface area of a cylinder is \(A = 2\pi rh\), where \(h\) is the height of the cylinder. Here \(h = 13.9\) cm and \(r = 5.8\) cm.

Step3: Substitute the values into the formula

\(A=2\times\pi\times5.8\times13.9\).
First, calculate \(2\times5.8\times13.9 = 2\times80.62=161.24\).
Then \(A = 161.24\pi\).
Using \(\pi\approx3.14159\), we have \(A=161.24\times3.14159\approx510.03\).

Answer:

510.03